Radical and its rational exponential form

[OceanSpring]

Can someone explain how these are equivalent.

sqrt((-3)^2) = (-3)^2/2

=sqrt(9) and (-3)^1

3 is not equal to -3

(-3)^2/2 can be expressed as:

(-3^2)^1/2 and (-3^1/2)2

(9)^1/2 and (sqrt(-1)sqrt(3))^2

3 is not equal to -3

Every textbook I've come across says these forms are equivalent. This seems totally inconsistent.

 

[mfb]

sqrt((-3)^2) = (-3)^2/2

That is not true. This rule applies to positive numbers in the inner bracket only.

In the complex numbers, you have to choose which root you would like to take (as there are always two, apart from sqrt(0), so sqrt(9)=-3 is... well, not completely wrong, but not really right.